Dear all and mentors,

I have background knowledge in math (graph theory, number theory, 
commutative algebra, and algebraic geometry) and computer science, so I am 
interested in the following two projects:

1. Improve Height Functionality
2. Edge connectivity and edge disjoint spanning trees in digraphs

However, I do have some questions that are not answered by the 
documentation and/or project descriptions. I was wondering that could you 
please help me clarify?

1. For the first project, it's mentioned that interested participants 
should know "basic algebraic geometry and number theory". So I was 
wondering that could you clarify more specifically what one needs to know: 
Does one need to know schemes and elliptic curves? Being able to read and 
understand Krumm's and Kutz15 [1] papers? First chapter of Hartshorne 
and/or "Ideals, Varieties, and Algorithms"?

2. While the second project is interesting on its own, I have a potential 
project idea to suggest: *Odd-cycle transversal* [0], which removes some 
vertices in a graph to make it bipartite.

After doing a simple search in the source code, I could not find anything 
related to this, so I think it may be a nice addition to Sage. I have 
experience implementing relevant approximation, heuristics, and (recent) 
FPT (fixed-parameter tractable) algorithms in Python (with networkx) and 
C++ as part of my undergraduate research project.

Thank you for your time.

Jing

[1]: https://en.wikipedia.org/wiki/Odd_cycle_transversal
[2]: https://arxiv.org/abs/1210.6246

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